Apparatus and method for evaluation of optical elements

ABSTRACT

An apparatus for measuring the optical performance characteristics and dimensions of an optical element comprising a low coherence interferometer and a Shack-Hartmann wavefront sensor comprising a light source, a plurality of lenslets, and a sensor array is disclosed. The low coherence interferometer is configured to direct a measurement beam along a central axis of the optical element, and to measure the thickness of the center of the optical element. The light source of the Shack-Hartmann wavefront sensor is configured to emit a waveform directed parallel to and surrounding the measurement beam of the interferometer, through the plurality of lenslets, and to the sensor array. A method for measuring the optical performance characteristics and dimensions of a lens using the apparatus is also disclosed.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation of copending U.S. patent applicationSer. No. 14/674,748, filed on Mar. 31, 2015 and issued as U.S. Pat. No.9,341,541 on May 17, 2016, which is a continuation of copending U.S.patent application Ser. No. 13/794,577, filed on Mar. 11, 2013 andissued as U.S. Pat. No. 9,019,485 on Apr. 28, 2015, the disclosures ofwhich are incorporated herein by reference.

BACKGROUND

1. Technical Field

The present invention relates to the metrology of optical elements, andin particular, the measurement of thickness, optical power and opticalaberrations of lenses.

2. Description of Related Art

In the manufacturing of lenses, obtaining fast and accurate measurementsof lens dimensions is a challenging problem. This is particularly thecase for small low cost high volume lenses, such as contact lenses forthe eye. Low-coherence interferometry (LCI) is one measurementtechnology that may be applied to this measurement problem.

LCI has applications in many fields from medical imaging to glassmanufacturing. The low-coherence interferometry is based on using alight source with a very short coherence length. The light is splitbetween two arms of an interferometer and then recombined and directedonto a detector. Interference occurs when the path lengths of the twoarms of the interferometer are equal to within the coherence length ofthe light from the source.

There are numerous known configurations of such interferometers, such asthe Michelson, Mach-Zehnder, and Fizeau interferometers, and othersdescribed in the text, Principles of Optics: Electromagnetic Theory OfPropagation, Interference and Diffraction of Light, M. Born and E. Wolf,Cambridge University Press, Cambridge; N.Y., 1999, 7th ed. Anotherexample of such an interferometer is described in U.S. Pat. No.6,724,487 of Marcus et al., “Apparatus and method for measuring digitalimager, package and wafer bow and deviation from flatness,” thedisclosure of which is incorporated herein by reference. (“Marcus '487”subsequently herein.)

The interferometer disclosed therein by Marcus '487 is based on the useof piezo fiber stretching technology as the means of changing theoptical path-length. A narrow beam of low-coherent light is directedonto the surface of the test object. It is common to focus the beaminside or in proximity to the test object. The reflected light from allof the object interfaces, which the beam traverses, is then collectedand analyzed by the interferometer. The interferometer is used toextract the optical distances between the interfaces. The physicaldistances are obtained by dividing the optical distances by the grouprefractive indices of the material which makes up the space between theinterfaces.

In a typical application, the light beam is directed along the opticalaxis of a lens. The axial thickness of the lens is then obtained bydividing the measured optical distance by the group refractive index ofthe glass or plastic material of the lens. Such measurement represents apoint measurement, since only the distance between the two points (pointof entry and exit of the measurement beam) is measured, while theinformation about the rest of the object (lens) is unknown.

When using LCI, it is possible, in principle, to move the measurementbeam laterally with respect to its axial propagation, and to measure thethickness of the object (lens) at different locations. However, thisapproach is associated with difficulties, arising from the LCIrequirements. One such requirement is to orient the measurement beamperpendicularly to the interfaces, to maximize the collection efficiencyof the reflected beam. Not only is this difficult to do when just oneinterface is present, but in the case of two or more non-parallelinterfaces (such as in a lens) such a requirement cannot befundamentally satisfied. For most lenses, the only locations in whichthe two lens surfaces are parallel and able to be positionedperpendicular to the measurement beam are near the center of the lens.In order for the LCI to be able to measure effectively, the reflectedlight coming back from the lens must be within the numerical aperture ofthe lens and optical fiber. For most lenses, only the central region ofthe lens can be measured by using LCI. This is insufficient for thecharacterization of many lens products.

A wavefront sensor is a device for measuring the optical aberrations ofan optical wavefront. This is accomplished by measuring the irradianceand phase distribution of the light beam at a particular plane in space.Although there are a variety of wavefront sensing technologies,including lateral shearing interferometers, curvature sensors, pyramidwavefront sensors, Focault knife-edge test, Ronchi test, andShack-Hartman Wavefront Sensor (SHWFS), the SHWFS has been the mostfrequently employed, since it is capable of measuring both irradianceand phase distributions in a single frame of data.

U.S. Pat. No. 5,936,720 by Daniel R. Neal et al. entitled “BeamCharacterization By Wavefront Sensor” issued on Aug. 10, 1999 and U.S.Pat. No. 6,130,419 by Daniel R. Neal “Fixed Mount Wavefront Sensor”issued on Oct. 10, 2000 describe the basics principles of operations ofa wavefront sensor employing a two dimensional Shack-Hartman lensletarray; the disclosures of these patents are incorporated herein byreference. Further details on the use of Shack-Hartman wavefront sensorsin optical metrology may be found in “Application of Shack-Hartmannwavefront sensing technology to transmissive optic metrology” by R. R.Rammage et al., Proc. SPIE Vol. 4779, Advanced CharacterizationTechniques for Optical, Semiconductor, and Data Storage Components, pp.161-172, (2002).

U.S. Pat. No. 7,583,389 by Daniel R. Neal et al. entitled “GeometricMeasurement System And Method Of Measuring A Geometric Characteristic OfAn Object” issued on Sep. 1, 2009, describes a white lightinterferometer to measure surface curvature and or thickness of anobject. This patent discloses the requirement of tilting of the objectwith respect to the interferometer apparatus and measuring at a varietyof tilt angles in order to characterize a single surface of the object.The disclosure of this patent is incorporated herein by reference.

U.S. Pat. No. 7,623,251 by Daniel R. Neal et al. entitled “GeometricMeasurement System And Method Of Measuring A Geometric Characteristic OfAn Object” issued on Nov. 24, 2009 describes the use of wavefrontsensing to measure surface curvature of an object on one or moresurfaces. The measurement requires moving the object relative to themeasurement apparatus and measuring at a variety of positions and/orangles in order to characterize the curvature of the one or moresurfaces. The disclosure of this patent is incorporated herein byreference.

The disclosures of these patents notwithstanding, there remains an unmetneed for a measurement apparatus and method that enables the non-contactmeasurement of lens or other optical element thickness and surfacecurvature of the top and bottom surfaces across a broad range oflocations on the lens surface, along with the measurement of the opticalaberrations of the lens or other optical component without the need ofmoving the lens or optical element with respect to the measurementapparatus during measurement. There also remains an unmet need to beable to measure the physical dimensions and optical performanceparameters of multifocal and toric lenses. Such a measurement wouldinherently be faster since the sample would be static or not movingduring the entire measurement procedure.

SUMMARY

In accordance with the present disclosure, the problem of measuring thephysical dimensions and optical performance parameters of a lens orother optical element without contacting the lens or other opticalelement using a single instrument is solved by an apparatus comprising alow coherence interferometer, a wavefront sensor and an analyzer. Theapparatus may further include a computer in signal communication withthe low coherence interferometer and the wavefront sensor. The computermay include an algorithm to calculate a plurality of thicknessdimensions of the optical element.

In a first aspect of the invention, an apparatus for measuring thephysical dimensions and one or more optical performance parameters of anoptical element is provided. The apparatus comprises a low coherenceinterferometer configured to direct a first beam of light along adefined axis of the optical element. The low coherence interferometer isadapted to measure the optical thickness of the optical element alongthe defined axis. The apparatus further comprises a wavefront sensorcomprised of a light source and a sensor array. The light source isconfigured to emit a second beam of light surrounding the first beam oflight which is directed through the optical element, and onto the sensorarray. The wavefront sensor is adapted to measure wavefront deviationsdue to the presence of the optical element. The apparatus also comprisesan analyzer to determine at least one of a physical dimension or anoptical performance parameter of the optical element from theinterferometer optical thickness measurement and the wavefront sensorwavefront deviations measurement.

In a second aspect of the invention a method for measuring the physicaldimensions and one or more optical performance parameters of an opticalelement is provided. The method comprises the steps of providing a lowcoherence interferometer configured to direct a first beam of lightalong a defined axis of the optical element, and providing aShack-Hartmann wavefront sensor comprising a light source, a pluralityof lenslets, and a sensor array. The light source is configured to emita second beam of light surrounding the first beam of light. The methodalso comprises the steps of directing the first beam of light along thedefined axis of the optical element and measuring the thickness of theoptical element along its defined axis using the low coherenceinterferometer. The method further comprises the steps of measuring thewavefront deviations due to the presence of the optical element usingthe Shack-Hartmann wavefront sensor and calculating at least one of aphysical dimension or optical performance parameter of the opticalelement.

In a third aspect of the invention, a method for measuring thedimensions of a lens comprising a first surface and a second surface isprovided. The method comprises the steps of measuring the thickness ofthe lens at the center of the lens with a low coherence interferometer;measuring the focal length of the lens with a Shack-Hartmann wavefrontsensor; communicating the thickness of the lens and the focal length ofthe lens to a computer; calculating the radius of curvature of the firstsurface of the lens and the radius of curvature of the second surface ofthe lens using an algorithm contained in the computer to obtain thedimensions of the lens, and performing at least one of storing in in anon-transitory computer storage medium, communicating externally, ordisplaying the dimensions of the lens on a display.

These and other aspects, objects, features and advantages of the presentinvention will be more clearly understood and appreciated from a reviewof the following detailed description of the preferred embodiments andappended claims, and by reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will be provided with reference to the followingdrawings, in which like numerals refer to like elements, and in which:

FIG. 1 shows a schematic block diagram of a lens or other opticalcomponent measurement apparatus in accordance with one embodiment of theinvention;

FIG. 1A shows an enlargement of the cuvette and lens under test shown inFIG. 1;

FIG. 1B shows an exemplary low coherence interferometer in a standardmode configuration in accordance a first embodiment of the invention;

FIG. 1C shows an exemplary low coherence interferometer in anautocorrelation mode configuration in accordance with a secondembodiment of the invention;

FIG. 2 shows an example of low coherence interferometer data obtainedduring measurement of a lens using the LCI apparatus of FIG. 1B;

FIG. 2A shows an example of low coherence interferometer data obtainedduring measurement of a lens using the LCI apparatus of FIG. 1C;

FIG. 3 shows a schematic illustration of a lens that may be measured bythe Applicants' measurement apparatus;

FIG. 4 shows an enlargement of a modified cuvette to measure a doubleconvex lens using the apparatus shown in FIG. 1;

FIG. 5 shows a flow diagram showing the steps used for characterizationof symmetric optical elements according to an embodiment of theinvention;

FIG. 6 shows a flow chart detailing the reference measurement step shownin FIG. 5 according to an embodiment of the invention; and

FIG. 7 shows a flow chart describing the steps used for characterizationof arbitrary optical elements according to an embodiment of theinvention.

The present invention will be described in connection with certainpreferred embodiments. However, it is to be understood that there is nointent to limit the invention to the embodiments described. On thecontrary, the intent is to cover all alternatives, modifications, andequivalents as may be included within the spirit and scope of theinvention as defined by the appended claims.

DETAILED DESCRIPTION

The present description is directed in particular to elements formingpart of, or cooperating more directly with, apparatus in accordance tothe invention. For a general understanding of the present invention,reference is made to the drawings. It is to be understood that elementsnot specifically shown or described may take various form well known tothose skilled in the art. Figures shown and described herein areprovided in order to illustrate key principles of operation of thepresent invention and are not drawn with intent to show actual size orscale. Some exaggeration, i.e., variation in size or scale may benecessary in order to emphasize relative spatial relationships orprinciples of operation.

In the drawings, like reference numerals have been used throughout todesignate identical elements. In the following disclosure, the presentinvention is described in the context of its use as an apparatus andmethod for measuring the thickness of lenses. However, it is not to beconstrued as being limited only to use in lens measurement. Theinvention is adaptable to many other uses for measurement of transparentobjects having non-parallel surfaces. Additionally, this description mayidentify certain components with the adjectives “top,” “upper,”“bottom,” “lower,” “left,” “right,” etc. These adjectives are providedin the context of use of the apparatus as a lens measurement device, andin the context of the orientation of the drawings, which is arbitrary.The description is not to be construed as limiting the apparatus to usein a particular spatial orientation. The instant apparatus may be usedin orientations other than those shown and described herein.

Turning now to FIG. 1, an exemplary embodiment of the Applicants'apparatus 100 for measuring the physical dimensions and one or moreoptical performance parameters of a lens or other optical component isshown. Using this apparatus 100, the absolute thickness distributionover the entire surface area of the lens 101 or other optical element101 can be determined as well as the top and bottom surface profiles andradii of curvature of each of the outer surfaces 116 and 118 of theoptical element 101. The index of refraction of the optical element 101is also measured. The optical performance characteristics that can bemeasured using this apparatus include optical power, focal length andoptical aberrations including spherical aberration, chromaticaberration, astigmatism, coma, field curvature, and distortion.

The apparatus 100 is comprised of a low coherence interferometer (LCI)108 and a Shack-Hartman wavefront sensor (SHWFS) 120. The opticalelement 101 under test is placed in a cuvette 102 or another type ofholder used to position the optical element 101 into the measurementlocation in the apparatus 100.

The optical element 101 may be a lens, e.g., a contact lens 101 forfitment to an eye. The low coherence interferometer 108 includes a lowcoherence light source which transmits low coherence light throughoptical fiber 136 which is input into optical probe 130. Optical probe130 directs and focuses the low coherence light, herein called a firstbeam of light 107, onto the optical element 101. Some of the first beamof light 107 passes through the optical element 101, and some of thefirst beam of light 107 is reflected off of each optical interface 116and 118 of the optical element 101. A transport mechanism 131 comprisinga pair of perpendicular transport stages and controllers is coupled tothe optical probe 130 which allows positioning of the optical probe 130so the first beam of light 107 is directed along a defined axis of theoptical element 101 during measurement. The term “defined axis” is usedto denote locations on the optical element 101 where the top and bottomsurfaces 116 and 118 of the lens/element 101 are most parallel.

The low coherence interferometer 108 is configured to direct a firstbeam of light or low coherence measurement beam 107 along an axis whichcoincides with the defined axis of the optical element 101, and tomeasure the thickness of the optical element 101 along the defined axis.When testing an axially symmetric optical element such as a sphericallens, the defined axis is preferably the center of the lens. Whentesting a cylindrical lens the defined axis may be centered anywherealong the cylinder's length. When testing an arbitrary optical element,the defined axis is any location where two or more surfaces of theoptical element are parallel. Multifocal and toric lenses can have morethan one defined axis.

The light source 103 of the Shack-Hartmann wavefront sensor 120 isconfigured to emit a second beam of light or wavefront light beam 104surrounding and encompassing and preferably directed parallel to themeasurement beam 107 of the interferometer 108, through a plurality oflenslets 115, and to a sensor array 106. The wavefront sensor 120 isadapted to measure wavefront deviations due to the presence of theoptical element 101. The wavefront deviations are measured over themeasurement window of the optical element 101 which is defined by theregion of the optical element 101 that is imaged onto the wavefrontsensor's sensor array 106.

During operation, an analyzer 112, which may be a computer, analyzesdata obtained by the wavefront sensor 120 and low coherenceinterferometer 108 to determine the physical dimensions and opticalperformance parameters of the optical element 101. The analyzer 112 canalso be utilized to determine the locations of the defined axes and toprovide feedback to the transport mechanism 131 to properly position thefirst beam of light 107 so that the LCI measurement can be performed atthe defined axes locations. The transport mechanism 131 has an encoder(not shown) which is calibrated to position the first beam of light 107at the same absolute locations onto the optical element 101 asdetermined by the wavefront sensor's sensor array 106. The wavefrontsensor 120 and the low coherence interferometer 108 share the samemeasurement window.

FIG. 1B and 1C show further detail of exemplary dual low coherenceinterferometers 108 that can be used in accordance with embodiments ofthe invention. FIG. 1B shows a standard mode interferometer 20 and FIG.1C shows an autocorrelation mode interferometer 20A. Parts with the samenumber in these two figures serve the same purpose. “Dual” refers to thefact that the instrument combines a laser interferometer with a lowcoherence interferometer as disclosed in Marcus '487. In a standard modeinterferometer 20 as shown fin FIG. 1B, the sample arm is in one arm ofa Michelson interferometer, while in the autocorrelation modeinterferometer 20A shown in FIG. 1C, light that is sent to the sample isreflected back into the Michelson interferometer.

In the standard mode dual interferometer 20 shown in FIG. 1B, lowcoherence light from a low coherence light source 21 is coupled intooptical fiber 27. Coherent light from coherent light source 22,typically a laser, is coupled into optical fiber 26. The coherent lightand low coherence light are combined by light combiner 23 and traveltogether along optical fiber 32 which is input into optical circulator24. An optical circulator is a three port device that functions as anoptical isolator and allows light to propagate in one direction from thefirst port to the second port of the circulator and from the second portto the third port of the circulator, but not in the reverse direction.The clockwise arrow inside circulator 24 is to indicate the direction inwhich light will propagate. As an example, light entering from opticalfiber 32 can travel into optical fiber 28, but not into optical fiber31.

The combined light traveling along optical fiber 32 which is input intothe optical circulator 24 exits the optical circulator 24 and travelsalong optical fiber 28 which is input into 2 by 2 coupler 36. Thecombined light passing through 2 by 2 coupler 36 is split and part ofthe combined light passes through each of the pair of fibers 37 whichmake up the two arms of a Michelson interferometer labeled R and S forreference arm and sample arm. Each arm of the Michelson interferometerhas a fiber stretcher 25 which is comprised of an optical fiber wrappedaround a piezoelectric cylinder which is used to change the path lengthin each of the two interferometer arms. The combined light travelsthrough fibers 37 then through the fiber stretchers 25 into opticalfibers 38 and through Faraday rotators 39. The Faraday rotators 39function to rotate the polarization of the beam to compensate for thechanges in phase of light which occur when light reflects from asurface.

In the reference arm R of the Michelson interferometer, the combinedlight passing through the Faraday rotator 39 becomes combined referencelight beam 40. Combined reference light beam 40 is incident upon mirror41 and is reflected back through the Faraday rotators 39 into opticalfiber 38, fiber stretcher 25, back along fiber 37 and back into 2 by 2coupler 36. In the sample arm S of the Michelson interferometer, thecombined light traveling through the Faraday rotator 39 becomes combinedlight beam 42 which is incident upon a dichroic beam splitter 43. Thedichroic beam splitter 43 is designed to reflect the coherent light aslaser light beam 45 and to transmit the low coherence light as lowcoherence light beam 46. The coherent light beam 45 is incident ontomirror 41 and is reflected back into the dichroic beam splitter and backinto the combined light beam 42, back through Faraday rotator 39, backinto optical fiber 38, back into fiber stretcher 25, back along fiber 37and back into 2 by 2 coupler 36. The low coherence light beam 46 passesthrough optical probe 130 and is incident on the sample chamber 44.Sample 44 is equivalent to the cuvette 102 shown in FIG. 1 and can beutilized with or without the optical element 101 under test installed init.

Light is reflected from each of the optical interfaces of the sample 44back into low coherence light beam 46, back through the optical probe130, passing back through the dichroic beam splitter 43, back throughcombined light beam 42, back through Faraday rotator 39, back throughoptical fiber 38, back into fiber stretcher 25, back along fiber 37 andback into 2 by 2 coupler 36. The low coherence light that returns fromeach optical interface in the sample arm S of the interferometer and thereference arm of the interferometer R are recombined and made tointerfere with each other as they enter 2 by 2 coupler 36. Constructiveinterference occurs when the optical path lengths of the two arms of theinterferometer are equal and when they differ by the distance betweenthe first and each of the other optical interfaces in the sample asdescribed below with reference to the discussion of FIG. 2.

Similarly the coherent light returning from the mirrors 41 in thereference arm R and the sample arm S of the Michelson interferometer arerecombined as they reenter 2 by 2 coupler 36 and interfere with eachother. Since the light is coherent, the interference pattern issinusoidal with a period of λ/2 where λ is the wavelength of thecoherent light source. Typically the zero crossings of the coherentlight interferometer signal is used as a constant distance intervaldistance scale for sampling of the low coherence interferometer signal.Since the coherent light and the low coherence light are in differentwavelength bands and are independent there is no mutual interferencebetween the two types of light. Thus the coherent light interference isindependent of the low coherence light interference.

After passing back through 2 by 2 coupler 36, the interfering coherentlight and the interfering low coherence light are each split into twocomponents traveling into optical fiber 29 and back through opticalfiber 28. The interfering light returning through fiber 28 then passesback into the circulator 24 and is sent into optical fiber 31. The lighttraveling through optical fiber 32 is incident on a laser blockingfilter 62, which passes the low coherence light as low coherence lightbeam 65, which is incident into one of the inputs of a balanced detector30. The laser light beam is blocked by laser blocking filter 62.

The light traveling through optical fiber 29 is incident on a dichroicfilter 66, which transmits the low coherence light as low coherencelight beam 35 and reflects the coherent light as coherent light beam 34.The low coherence light beam 35 is incident onto the second input of thebalanced detector 30, while the coherent light beam 34 is incident ontolaser detector 33. FIG. 2 shows an example of low coherenceinterferometer data obtained while measuring a lens mounted in a cuvetteafter amplifying and filtering the signal received from the balanceddetector 30 using the LCI apparatus of FIG. 1 B.

FIG. 1C shows a dual interferometer in an autocorrelation mode. In thiscase light reflecting from the sample is input to both arms of aMichelson interferometer M1 and M2. Light from low coherence lightsource 21 is coupled into optical fiber 27, then passes throughcirculator 24 into optical fiber 28 through wavelength divisionmultiplexer 55 into optical fiber 54, and then passes through opticalprobe 130 to form a low coherence light beam 46 which is incident on thesample 44. Low coherence light reflected off of each optical interfacein the sample returns opposite to low coherence light beam 46 backthrough optical probe 130 into optical fiber 54, then wavelengthdivision multiplexer 55, then back through optical fiber 28 and backinto circulator 24. The light reflected off of each optical interface ofthe sample passes through circulator 24 into optical fiber 49 and theninto the dual Michelson interferometer section of the interferometerapparatus 20A as it passes through wavelength division multiplexer 57where it is combined with coherent light from coherent light source 22traveling along optical fiber 26.

Combined light consisting of the low coherence light reflected from eachof the optical interfaces in the sample 44 and the coherent light fromcoherent light source 22 from wavelength division multiplexer 57 travelsalong optical fiber 58 and into 2 by 2 coupler 36 where the light issplit into 2 beams to travel along optical fibers 59 which make up thetwo arms M1 and M2 of the Michelson interferometer. Combined lighttraveling along optical fibers 59 are sent through the fiber stretchers25 into optical fibers 38 and through Faraday rotators mirrors 47. TheFaraday rotator mirrors 47 combine a Faraday rotator with a mirror. Thecombined light in each interferometer arm is reflected off of theFaraday rotator mirrors 47 and travels back along optical fibers 38through fiber stretches 25 and optical fibers 59.

The respective reflected combined light streams in each arm M1 and M2are recombined as they enter 2 by 2 coupler 36. The low coherence lightreturning from both arms M1 and M2 of the interferometer are recombinedand made to interfere with each other as they enter 2by 2 coupler 36.Constructive interference occurs when the optical path lengths of thetwo arms of the interferometer are equal and when they differ by thedistance between different optical interfaces in the sample as describedbelow with reference to the discussion of FIG. 2A. Similarly thecoherent light returning from both arms M1 and M2 of the interferometerare recombined as they reenter 2by 2 coupler 36 and interfere with eachother. As in the case of the apparatus 20 shown in FIG. 1 B, thecoherent light interference pattern is sinusoidal with a period of λ/2where λ is the wavelength of the coherent light source, and the zerocrossings can be used as a constant distance interval scale for samplingof the low coherence interferometer signal.

As described previously for interferometer 20 of FIG. 1B, the lowcoherence light interference and the coherent light interference aremutually independent. Combined interfering coherent and low coherencelight which passes back through 2by 2 coupler 36 is coupled into opticalfiber 53 and enters wavelength division multiplexer 48 which separatesthe low coherence light from the coherent light. The interfering lowcoherence light is sent through optical fiber 52 and is incident ondetector 50 through optional filter 61 which blocks any remainingcoherent light from entering the low coherence light detector 50. Theinterfering coherent light is sent through optical fiber 51 and isincident on detector 33 through optional filter 63 which blocks anyremaining low coherence light from entering the coherent light detector33. FIG. 2A shows an example of low coherence interferometer dataobtained while measuring a lens mounted in a cuvette after amplifyingand filtering the signal received from detector 50 using the LCIapparatus of FIG. 1C.

Using the apparatus 100, the optical power, the physical dimensions andoptical aberrations of a contact lens may be measured. Optical power andoptical aberrations define the optical performance parameters of a lens.Examples of optical aberrations are spherical, chromatic, astigmatism,coma, field curvature, distortion and others. In optics, the termwaveform is used to denote the amplitude and phase of a light beam as afunction of time and position. The wavefront of a light beam is definedas the locus of points having the same optical phase. The wavefront of alight beam can be defined as the virtual surface defined by the pointson all possible rays in a light beam having equal optical path lengthfrom a spatially coherent source. As examples the wavefront of lightemanating from a point light source is a sphere, and the wavefrontcreated by an ideal collimating lens mounted at its focal length from apoint source is a plane.

Referring again to FIG. 1, the SHWFS 120 is comprised of an array 105 ofclosely spaced microlenses 115 (referred to herein as a lenslet array)to probe the incoming wavefront, i.e., the light directed to the array105. The lenslet array 105 focuses the incoming light into an array offocal spots 117. The location of the spots 117 depends on theorientation of the incoming wavefronts. As such, the lenslet array 105translates the phase of the incoming light into a lateral shift of thefocal spots 117.

The SHWFS 120 is further comprised of a sensor array 106 such as a2-dimensional CCD or CMOS imager, which is used to determine thelocations and extent of the shift of the focal spots 117. The amount ofshift of each spot 117 may then be used to find wavefront orientation ateach respective lenslet 115 location. From this information, the overallwavefront can then be reconstructed. Further details on the use of aShack-Hartman wavefront sensor in optical metrology may be found in“Application of Shack-Hartmann wavefront sensing technology totransmissive optic metrology,” R. R. Rammage et al., Proc. SPIE 4779,Advanced Characterization Techniques for Optical, Semiconductor, andData Storage Components, 161. One may also refer to U.S. Pat. Nos.5,936,720, “Beam characterization by wavefront sensor,” and 6,130,419,“Fixed mount wavefront sensor,” the disclosures of which areincorporated herein by reference.

When an optical element 101, such as contact lens 101, is tested andmeasured using the apparatus 100, a known waveform is directed onto theelement 101. The transmitted waveform is analyzed using the SHWFS 120,and the difference between the incident and transmitted waveforms isused to extract optical properties of the element 101. As an example,the lens focal length can be calculated from data provided by the SHWFS120 as described in the article, “Measurement of lens focal length usingmulti-curvature analysis of Shack-Hartmann wavefront data”, Daniel R.Neal, James Copland, David A. Neal, Daniel M. Topa, Phillip Riera, Proc.of SPIE Vol. 5523, pp. 243-255, (2004), subsequently referred to hereinas Neal et al. When the physical information about the element 101 isnot known exactly, i.e. it is not possible to construct the physicalmodel of the element 101 based purely on the wavefront analysisperformed by the SHWFS 120 alone. For example, the lens thickness andthickness variations throughout the lens 101 as well as the lens indexof refraction and individual radii of curvature of the surfaces 116 and118 making up the lens cannot be obtained using only the SHWFS 120.

Advantageously, however, the combination of the LCI 108 and the SHWFS120 in the Applicants’ apparatus 100 enable the measurement of opticalelement thickness and optical performance parameters. This will now beexplained with reference to FIG. 1 and FIG. 1A, using the example ofmeasurement of a contact lens. It is to be understood that that thedefined axis is the center of the lens 101 for the purposes of thediscussion that follows.

Referring to FIG. 1A, details of the lens 101 mounted into the cuvetteor holder 102 are shown. The lens 101 having an index of refractionn_(l) and central thickness t_(l) is placed inside the glass or plasticcuvette 102 with its concave surface 116 oriented downwardly, and itsouter edge in contact with an inner surface 113 of the cuvette bottomsection 102B. During measurement, the cuvette 102 is filled with asolution 121 having index of refraction n_(s). Referring also to FIG. 1,the SHWFS 120 is further comprised of a light source 103 and a lens 114,which produce a second beam of light 104 with a known incident waveformhaving incident wavefront indicated by arrows 132. The light beam 104passes through a dichroic mirror 109 and illuminates the lens 101. Thelight beam 104 passes through the top section 102T of the cuvette, thelens 101 and the bottom section 102B of the cuvette and is focused bythe lenslet array 105 onto the sensor array 106.

In cases where all surfaces of the cuvette 102 are precision parallelsurfaces they will have no effect on the wavefront of the lighttransmitted through the cuvette. In cases where the surfaces are notexactly flat and parallel, the wavefront W_(l) can be measured with thecuvette 102 alone, and then with the lens present inside the cuvette,W_(L+r). The differences between the wavefronts measured with the lensinside the cuvette and the cuvette alone are then analyzed to arrive atthe wavefront deviations W_(l) due to the lens. As a general practice, areference wavefront W_(r) is first measured through the cuvette withoutthe lens being present before measuring the wavefront W_(l+r) with thelens or other optical element being present.

The wavefront deviations due to the lens are then calculated and thenanalyzed to determine the lens focal length and optical performanceparameters of the lens which include the optical aberrations of thelens. The optical performance parameters of the lens that can beanalyzed include spherical aberration, chromatic aberration,astigmatism, coma, field curvature and distortion. Of particularimportance is the slope of the wavefront deviations due to the lens.Locations on the lens surface at which the slope of the wavefrontdeviations is zero are locations where the two surfaces of the lens areparallel. The locations at which the slope of the wavefront deviationsare zero coincide with the defined axes of the lens. The locations ofthe defined axes are locations at which the thickness of the lens willbe measured with the low coherence light interferometer. For a sphericallens the location at which the slope of the wavefront deviations fromthe lens is zero corresponds to the center of the lens.

The low coherence light from LCI 108 is coupled to optical fiber 136 andis transmitted through optical probe 130 to direct a low coherence lightbeam 107 to the dichroic mirror 109 or other coupler, thereby combiningthe low coherence light beam 107 with the wavefront sensor light beam104. In order to allow concurrent operation of the low coherenceinterferometer 108 and the SHWFS 120 the first beam of light 107 and thesecond beam of light 104 should be in distinctly different wavelengthregions of the optical spectrum.

For example, the low coherence interferometer 108 may have a lightsource centered at around 1300 nm with a bandwidth of 30-100 nm and theSHWFS may have a light source in the visible part of the spectrum(400-700 nm). In this case, as shown in the embodiment of FIG. 1, thedichroic mirror 109 transmits light at wavelengths below a cutoffwavelength and reflects light at wavelengths above the cutoffwavelength. The light source 103 in apparatus 100 is used produce lightof wavelengths predominately below the cutoff wavelength while the lowcoherence light beam is comprised of light entirely of wavelengths abovethe cutoff wavelength.

In a second example it is possible for the low coherence light source tobe centered in the visible part of the spectrum and the SHWFS to be inthe NIR part of the spectrum. In this case, the dichroic mirror 109would transmits light at wavelengths above a cutoff wavelength andreflect light at wavelengths below the cutoff wavelength. The first beamof light 107 is then sent through the top section 102T of cuvette 102,the lens 101, and the cuvette bottom section 102B. A portion of thelight beam 107 is reflected off of each of the optical interfaces thatlight beam 107 passes through and the reflected light that couples backinto the optical probe 130 and back through optical fiber 136 and intothe interferometer 108 is analyzed.

Optical probe 130 is preferably designed to focus light inside of thecuvette or holder 102. The optical reflections that are analyzed includethe bottom or inner surface 124 of the cuvette top section 102T alsocalled the first inner surface, the lens convex surface 118, the lensconcave surface 116 and the top or inner surface 113 of the cuvettebottom section 102B also called the second inner surface. For thepurposes of this discussion it is assumed that the thickness of the topand bottom surfaces of the holder 102T and 102B respectively are largeenough so that the only reflections that occur in the interferometerscans from the holder 102 are from the optical interfaces that at thefirst inner surface 124 and the second inner surface 113.

The LCI 108 is used to calculate the central thickness 110 of lens 101defined as t_(l), as well as the distance 111 between concave surface116 of lens 101 and inner cuvette surface 113 of cuvette bottom section102B defined as S and distance 123 between the convex surface 118 oflens 101 and inner cuvette surface 124 of cuvette top section 102Tdefined as G in FIG. 1A. During operation, the low coherenceinterferometer 108 measures optical distances between each of theoptical interfaces in the sample. The cuvette physical path length is d,at the location of the measurements. This can be measured in air firstproviding a result of n_(a)d_(o) for the measured cuvette optical pathlength. The cuvette's physical path length d_(o) is then determined bydividing the cuvette's measured optical path length (n_(a)d_(o)) by theknown index of refraction of air n, at the wavelength of the lowcoherence light source.

The index of refraction of the solution n_(s) at the measurementwavelength of the low coherence light source can then be determined byfilling the cuvette 102 with solution 123. The measured optical path isnow n_(s)d_(o). The solution's index of refraction n_(s) at thewavelength of measurement is then determined by dividing the measuredoptical path length of the cuvette filled with solution (n_(s)d_(o)) bythe cuvette's physical path length d_(o). Once the physical path lengthd_(o) of the cuvette and the index of refraction n_(s) of the solutionare known, they can be used as constants in the calculations for lensindex of refraction n_(l) and lens thickness t_(l).

When a lens is inserted into the measurement apparatus 100 and isproperly centered, the measured optical distances are n_(s)G, theoptical thickness corresponding to distance 123, n_(l)t_(l) the measuredoptical thickness corresponding to lens center thickness 110 of lens 101and n_(s)S, the measured optical distance corresponding to distance 111as shown in FIG. 1A. FIG. 2 shows sample LCI data obtained using astandard mode interferometer such as the one shown in FIG. 1B during themeasurement of a lens mounted in a cuvette filled with solution. Thex-axis is in units of relative difference in length between the two armsof the interferometer in microns and the y axis is the intensitymeasured. Successive peaks in the interferometer trace occur when thepath length of the reflected beam in the reference arm R is equal to thepath length of the reflected beam from the sample arm S, which occur ateach optical interface in the sample.

We define the measurement region as the region of interest in the testoptical component plus optical component holder (lens surfaces+cuvetteinner surfaces). The first peak from left to right shown in theinterferometer trace of FIG. 2 is from the optical interface occurringat the inner surface 124 of cuvette top 102T. Similarly, the second peakfrom left to right is from the lens convex surface interface 118, thethird peak from left to right is from the lens concave surface 116 andthe fourth peak from left to right is from the top surface 113 ofcuvette bottom 102B. The measured parameters n_(s)G, n_(l)t_(l) andn_(s)S which are defined as the distances between adjacent peaks in theinterferometer data are shown in FIG. 2 using a standard mode lowcoherence interferometer. FIG. 2A shows similar data for a low coherenceinterferometer configured in an autocorrelation mode. The lens thicknesst_(l) and index of refraction n_(l) are calculated from therelationships

t _(l) =d _(o)−(n _(s) S)/n _(s)   (1) and

n _(l)=(n _(l) t _(l))/t _(l)   (2)

in which the parameters shown in parenthesis are the measured valuesshown in FIG. 2 and FIG. 2A.

FIG. 2A shows sample LCI data obtained using an interferometerconfigured in the autocorrelation mode such as the one shown in FIG. 1Cduring the measurement of a lens mounted in a cuvette filled withsolution with the measured parameters which are defined as the distancesbetween adjacent peaks in the interferometer data. The x axis is thepath length difference between the two arms of the interferometer inmicrons and the y axis is the intensity measured. Since the sample is inthe input arm of the interferometers, reflections occurring at each ofthe optical interfaces of the sample interfere with each other in theautocorrelation interferogram as shown in FIG. 2A. The interferogram issymmetric about the origin which is defined as the location at which thepath lengths of the two arms of the interferometer are equal. When thetwo arms of the interferometer M1 and M2 in FIG. 1C have equal pathlengths all of the optical interfaces in the sample interfere with eachother causing the zero crossing beak to have the largest amplitude. Asthe path lengths of the two arms in the interferometer are changed,peaks occur in the autocorrelator interferogram at optical pathdifferences equal to optical distances between the various surfaces inthe measurement region in order of increasing optical path differencebetween the surfaces. For the case of the lens shown in FIG. 1A mountedin cuvette 102, peaks occur at optical path differences of ±n_(l)t_(l),±n_(s)S, ±(n_(s)S+n_(l)t_(l)), ±n_(s)G, ±(n_(s)G+n_(l)t_(l)) and±(n_(s)S+n_(l)t_(l)+n_(s)G) in order of increasing (decreasing) opticalpath difference between optical interfaces in the measurement region ofthe optical component under test.

The data from the SHWFS 120 and the LCI 108 are communicated to ananalyzer which may be comprised of a computer 112, which furtheranalyzes the data and displays the results on display 119. The computercan be used for external communications and also comprises anon-transitory storage medium such as a hard drive which can be used forpermanent storage of the data. (As used herein, the term “non-transitorystorage medium” is meant to include all computer-readable media exceptfor a transitory, propagating signal.) The analyzer also is used toprovide feedback to the transport mechanism 131 to adjust the positionof optical probe 130 to the proper defined axes measurement locations atwhich LCI measurements are performed.

On a fundamental level, the following equation may be used to determinethe dimensions of the lens 101:

$\begin{matrix}{\frac{1}{f} = {{\left( {n_{l} - 1} \right)\left\lbrack {\frac{1}{R_{1\;}} - \frac{1}{R_{2}} + \frac{\left( {n_{l} - 1} \right)t_{l\;}}{n_{l}R_{1}R_{2}}} \right\rbrack} = P}} & (3)\end{matrix}$

where P is the optical power of the lens, f is the focal length of thelens, R₁ is the radius of curvature of the lens surface closest to thelight source and R₂ is the radius of curvature of the lens surfacefarthest from the light source. The sign of the lens' radii of curvatureindicate whether the corresponding surfaces are convex or concave. R₁ ispositive if the first surface is convex, and R₁ is negative if the firstsurface is concave. The signs are reversed for the second surface of thelens: R₂ is positive if the second surface is concave, and R₂ isnegative if the second surface is convex. Additionally, referring toFIG. 3, the convex surface 118 of the lens 101 being measured is definedby sphere 201 having a radius of curvature 203 shown as R₁.Correspondingly, the concave surface 116 of the lens being measured 101is defined by sphere 202 having a radius of curvature 204 shown as R₂.Also, n_(l) is the refractive index of the lens material, and t_(l) isthe central thickness 110 of the lens 101.

When R₁, R₂, and t_(l) are known, all physical dimensions of the lenscan be determined. If the lens outer diameter a₁ and inner diameter a₂defined in FIG. 1A as 126 and 127 respectively are measured along withthe lens thickness t_(l) and the distance S, the radii of curvature R₁and R₂ can be calculated from the relationships

$\begin{matrix}{{R_{1} = {{\left( {\frac{a_{1}^{2}}{4} + \left( {S + t_{l}} \right)^{2}} \right)/2}\left( {S + t_{l}} \right)}}{and}} & (4) \\{R_{2} = {{\left( {\frac{a_{2}^{2}}{4} + S^{2}} \right)/2}S}} & (5)\end{matrix}$

The lens inner and outer diameters a₁ and a₂ can be measured using theSHWFS or with an optional external image sensor 134 combined with theSHWFS as shown in FIG. 4. An optional beam splitter 128 is used toreflect a small percentage of the light beam 104 as reflected light beam135. Referring also to FIG. 1, reflected light beam 135 passes throughimaging lens 133 to form an image of the lens or optical element in thecuvette or holder on external image sensor 134. An image analyzer (notshown) is associated with the external image sensor 134 which receivesimages from the external image sensor 134 and can be configured todetermine the diameter of the optical element 101. The diameters a₁ anda₂ can be calculated by counting the number of pixels between the innerdiameters and outer diameters respectively and the known magnificationfactors of the imaging lens 133.

The image analyzer associated with the external image sensor 134 canalso be configured to receive images from the external image sensor 134in order to inspect the optical element 101 for defects. The focallength of a concave, convex lens or a double concave lens can bedetermined from the lens diameter measurement and the interferometercenter thickness and index of refraction measurement. The external imagesensor 134 can also be used to determine the location of the center ordefined axis of the lens under test or other optical element. Thecoordinates can then be communicated via the analyzer 112 to move thetransport mechanism 131 to properly position the first beam of light 107at the defined axis location.

The apparatus shown in FIG. 1 can also be used to measure the physicaland optical properties of double convex lenses as shown in FIG. 4. Thelens 101 in FIG. 1 and FIG. 1A has been replaced with a double convexlens 137 having top convex surface 140 with radius of curvature R_(T)and bottom convex surface 129 with radius of curvature R_(B). Thecuvette 102 now includes a lens holder insert 138 having an innerdiameter 139 defined as a₃ and having a height h_(h). The radius ofcurvature R_(B) of lens 137 bottom convex surface 129 can be calculatedusing the relationship

$\begin{matrix}{R_{B} = {{\left( {\frac{a_{3}^{2}}{4} + \left( {h_{h} - S} \right)^{2}} \right)/2}\left( {h_{h} - S} \right)}} & (6)\end{matrix}$

In the case of measurement of double convex lenses, the low coherenceinterferometer 108 is used to measure S, the thickness of the lens t_(l)and the index of refraction of the lens n_(l). The radius of curvatureR_(B) of the bottom convex surface 129 is calculated using the knownvalues for a₃ and h_(h) and the measured value of S. The focal length ofthe lens can be measured from analysis of the wavefront data obtainedwith the wavefront sensor 120 as described in the reference by Neal etal. The radius of curvature R_(T) of the upper convex lens surface 140can then be calculated using equation 3.

When measuring double convex lenses, the external image sensor 134 isnot required to measure the lens diameter. If the lens diameter isknown, or measured with the external image sensor 134, then the top andbottom radii of curvature of the double convex lens 137 can bedetermined using the diameter information and the interferometerthickness and index of refraction measurement. The above equations canbe programmed into an algorithm contained in computer 112, such that thedimensions of the lens 101 or other lenses can be calculated, stored inmemory, communicated externally, and/or displayed on display 119.

In circumstances where the surfaces of the lens cannot be accuratelydescribed by two perfect intersecting spheres, corrections must be addedto the above equations, to account for the deviations from perfectspheres. Such corrections may also be included in the algorithm executedby the computer 112.

The above method can be generalized to the measurement of thickness ofany arbitrary shaped lens or optical component as a function of positionon the optical component. This can be accomplished as long as the numberof variables that are needed to analytically describe the top and bottomsurfaces of the optical component is less than the resolution providedby the wavefront sensor.

Referring again to FIG. 1, the optical probe 130 may be mounted onto atransport mechanism indicated by arrows 131 to properly position thefirst beam of light 107 so that it coincides with the defined axis orcenter of the lens when thickness measurements are performed with thelow coherence interferometer 108. In the case of the contact lens 101,the center of the lens would have the largest measured opticalthickness. When the optical element under test has more than one definedaxis, lens thickness measurements can be performed at each of thedefined axes locations on the optical element. The thickness around asmall region around each defined axis may also be measured to determinethe position of the minimum or maximum thickness and to maximize orminimize the gap S. The transport mechanism 131 is may operate along twoaxes, and may include a position encoder (not shown) that is calibratedso that the position of first beam of light 107 on the optical elementunder test corresponds to the same position on the optical element 101as determined from the SHWFS data. Alternatively, the optical cell orcuvette 102 could be mounted onto the transport mechanism 131 toposition the lens at the defined or center axis or axes.

FIG. 5 and FIG. 6 show flow diagrams 300 and 310 describing the stepsused for characterization of symmetric optical elements according to theembodiment of the invention shown in FIG. 1. For the purposes of thediscussion of the flow chart in FIG. 5, it is assumed that the symmetricoptical element under test can be readily centered in the cuvette ormeasurement cell, and that the defined axis can be readily located.Arrows between adjacent steps in the flow diagrams indicate the orderthat the steps are performed while dotted arrows between adjacent stepsindicate that there is one or more steps that may be performedconcurrently or in any order or after the preceding step as describedbelow. Arrows 318 indicate steps that can be performed concurrently orin any order, and arrows 319 are calculation dependency indicators.Steps with calculation dependency indicator arrows 319 entering the stepbox are dependent on previous calculated or measured values. The stepsequences shown in FIGS. 5 and 6 are example sequences and are not meantto be limiting as will be described in the ensuing discussion of FIG. 5and FIG. 6.

The first step 310 shown in FIG. 5 measures and calculates the referenceparameters d_(o), n_(s) and the reference wavefront W_(r) and is calledthe reference measurement step. Further details of reference measurementstep 310 are shown in FIG. 6. The reference measurement step detailshown in FIG. 6 is broken up into further steps 320-327. In step 320 acuvette 102 appropriate for the size of the optical elements to bemeasured is installed in the instrument shown in FIG. 1. Step 320 isshown to be followed by Step 321 in which the optical path length in air(n_(a)d_(o)) of the cuvette is measured using the low coherenceinterferometer 108. Step 322 follows Step 321 in which the cuvette'sphysical path length d_(o) is then calculated by dividing the cuvette'smeasured optical path length in air by the index of refraction of air atthe measurement wavelength of the LCI. Step 323 follows Step 322 inwhich lens measurement solution is added to the cuvette. Step 324follows Step 323 in which the cuvette's optical path length in solution(n_(s)d_(o)) is measured using the low coherence interferometer.Following Step 324 is Step 325 in which the index of refraction of thesolution n_(s) is calculated by dividing the cuvette's measured opticalpath length in solution by the cuvette's physical path length d_(o). Thereference wavefront W_(r) is measured in Step 326 using the Shack HarmanWavefront Sensor (SHWFS). The reference values are saved and stored forlater use in subsequent calculations using the computer (step 327). Step326 is independent of steps 321-325 as indicated by concurrent stepindicator 318 and can occur either concurrently or before or after anyof the steps 321-325 in sequence. Optional concurrent step indicator318A is used to show that step 326 can be performed with the cuvettefilled with either air or solution since it is assumed that the solutionis homogeneous and will not affect the reference wavefront.

Referring back to FIG. 5, once the reference parameters d_(o), n_(s) andW_(r) are measured, the details of the further operations are dependentupon the shape of the bottom surface of the lens or other opticalcomponent under test. Step 301 of FIG. 5 is a decision step in whichsteps 302-307 shown on the left side of FIG. 5 are performed if thebottom surface of the lens under test is concave, while step 312-317shown on the right side of FIG. 5 are performed if the bottom surface ofthe lens under test is convex or flat. Types of optical elements inwhich Steps 302-307 are followed include concave-planar, convex-concaveand double concave lenses. For the case of a lens with at least oneconcave surface the lens is centered in the cuvette as indicated in Step302 with the concave surface facing downward as shown in FIG. 1A. Step303 is shown to follow Step 302 in which the lens inner diameter a₂ andthe lens outer diameter a₁ are measured using either the SHWFS orexternal imager. As indicated by the concurrent step indicator 318,steps 304 and/or 306 can also be performed simultaneously with Step 303.Also steps 303, 304 and 306 may be performed in any order. In Step 304which is shown to follow Step 303, the low coherence interferometer(LCI) measures the optical thickness of the lens n_(l)t_(l), the opticaldistance n_(s)G and the optical distance n_(s)S as described above inthe discussion of FIG. 1A and FIG. 2. The measurements made in Step 304can also be used to verify that the LCI measurement is being performedat the center of the lens by adjusting the position of the first beam oflight 107 using transport mechanism 131 to maximize the distance n_(s)S.Step 305 follows Step 304 in which the parameters tl, n_(l), S, G, R₂,R₁ and f are calculated using equations 1-5 described above. In step306, the SHWFS measures the wavefront W_(l+r) of the lens centered inthe cuvette. Step 306 is followed by Step 307 in which the wavefrontdeviations due to the lens W_(l) are calculated and the lens aberrationsare quantified using a wavefront analysis algorithm. The focal length ofthe lens f which was calculated in step 305 from the LCI data can alsobe calculated using the wavefront analysis algorithm during theperformance of Step 307. If the two independent calculations of lensfocal length f disagree, the lens most likely is not centered properlyduring the LCI measurement. During the performance of Step 307, thelocation at which the slope of W_(l), the wavefront deviations of thelens is zero can also be used to verify that the LCI measurement isbeing performed at the center of the lens. If the location is incorrect,the position of the first beam of light 107 can be adjusted to theproper location using transport mechanism 131 as determined from theslope measurement of the SHWFS. The LCI measurements in Step 304 canthen be repeated and the data reanalyzed. Although Step 306 withfollowing step 307 are shown to occur after Step 305 in FIG. 5, they areindependent of steps 303-305 and can occur either concurrently or beforeor after any of the steps 303-305 in sequence. Also, Step 304 isindependent of Step 303 and they can occur either concurrently or in anyorder. The calculation dependency indicator 319 on the left side of FIG.5 shows that the parameters obtained during performance of step 303 arerequired for obtaining the parameters in steps 305 and the valuesobtained during the performance of step 305 are useful for thecalculations performed in step 307.

Referring again to step 301 in FIG. 5, when the bottom surface of thelens or other optical element is not concave, Steps 312-317 areperformed to carry out the method of this embodiment of the invention.Types of optical elements in which steps 312-317 of FIG. 5 are performedinclude planar convex and double convex lenses. If the lens does nothave a concave surface, Step 312 is performed by installing a lensholder insert into the cuvette with known height h_(h) and diameterbetween the insert posts a₃ as shown in FIG. 4. The lens is thencentered on the lens holder insert. Step 312 is shown to be followed bystep 313 in which the low coherence interferometer measures the opticalthickness of the lens n_(l)t_(l), the optical distance n_(s)G and theoptical distance n_(s)S as described above in the discussion of FIG. 1Aand FIG. 2. Step 313 can also be used to verify that the LCI measurementis being performed at the center of the lens by adjusting the positionof the first beam of light 107 using transport mechanism 131 to minimizethe distance n_(s)S and maximize the optical thickness n_(l)t_(l) of thelens. As indicated by the concurrent step indicator 318, steps 313 and315 can also be performed simultaneously or in any order. Step 314follows Step 313 in which the parameters t_(l), n_(l), S, G, and R_(B)are calculated using equations 1-2 and equation 6 described above. Instep 315, the SHWFS measures the wavefront W_(l+r) of the lens centeredin the cuvette. Step 315 is followed by Step 316 in which the wavefrontdeviations due to the lens W_(l) are calculated and the lens aberrationsare quantified using a wavefront analysis algorithm. The lens focallength is also determined during step 316 from the wavefront analysisalgorithm. During the performance of Step 315, the location at which theslope of W_(l), the wavefront deviations of the lens is zero can also beused to verify that the LCI measurement is being performed at the centerof the lens. If the location is incorrect, the position of the firstbeam of light 107 can be adjusted to the proper location using transportmechanism 131 as determined from the slope measurement of the SHWFS. TheLCI measurements in Step 313 can then be repeated and the datareanalyzed. Step 316 is followed by Step 317 in which the radius ofcurvature of the top surface of the lens R_(T) is determined. R_(T) canbe determined from equation 3 by substituting R₂=R_(B) and R₁=R_(T) andusing the calculated values for f and R_(B). Although Step 315 withfollowing Step 316 are shown to occur after Step 314 in FIG. 5, they areindependent of Steps 313-314 and can occur either concurrently or beforeor after any of the Steps 313-314 in sequence. As above, the calculationdependency arrow 319 on the right side of FIG. 5 shows theinterdependencies between the various measured and calculated values.

FIG. 7 shows a flow chart 400 describing the steps used forcharacterization of arbitrary optical elements according to anembodiment of the invention. The first step 410 shown in FIG. 7 measuresand calculates the reference parameters d_(o), n_(s) and the referencewavefront W_(r) and is called the reference measurement step in the samemanner as Step 310 in FIG. 5 and FIG. 6. Step 410 is followed by step420 in which the optical element is installed into the test fixturewhich may be an optical cell or cuvette. Step 420 is followed by Step430. In Step 430 the wavefront of the optical element is measured usingthe SHWFS or other wavefront sensor. Step 430 is followed by Step 440 inwhich the wavefront deviation due to the lens is calculated as well asthe slopes of the wavefront deviation. Locations of the zeros in theslope are determined to identify the positions of the one or moredefined axes. Step 440 is followed by Step 450. In step 450 thetransport mechanism 131 is positioned so that the first beam of light107 passes through the location of the first defined axis. The LCImeasurement is then performed at the location of the first defined axisof the optical element. The optical thickness, gaps and index ofrefraction of the optical element at the location of the first definedaxis are then calculated from the LCI data. If there is more than onedefined axis, Steps 450 and 460 are repeated until all the defined axeslocations have been measured. This is indicated by repeat dotted arrowStep 455. Once all of the defined axes locations have been measured toprovide the physical thickness and height of the bottom surface and topsurface of the optical element at the defined axes locations, Step 470is performed which combines and analyzes the wavefront data obtained instep 430 together with the LCI data obtained in step 460 to calculatethe physical dimensions and optical performance parameters of theoptical element.

The apparatus and method of this invention provide much more informationconcerning the physical dimensions and optical performance parameters ofan optical element than can be determined by wavefront sensing and lowcoherence interferometry alone or when measured independently of eachother. The low coherence interferometer and the wavefront sensor sharethe same measurement window on the optical element and work incollaboration with each other to provide recursive feedback between thetwo measurement devices.

As an example in the measurement of a spherical lens, the wavefrontsensor is used to determine the location of the defined axis and alsomeasures the focal length and diameter of the lens. The first beam oflight of the low coherence interferometer is moved to the defined axislocation and the index of refraction n_(l) and thickness of the lens atthe defined axis location t_(l) is measured and the focal length f ofthe lens is calculated from the diameter of the lens G, S and n_(l)t_(l)along with the calculated radii of curvature R₁ and R₂ of the lens. Thefocal lengths of the lens determined from the wavefront sensor alone andfrom the interferometer alone are then compared, and the measurementlocation of the defined axis is readjusted recursively until the twosets of measurements agree.

In the case of measurement of multifocal optical elements, thecollaborative nature of the instruments allows the location of each ofthe defined axes to be determined along with the shape and physicaldimensions of the optical element. Combining the instrument withlocation feedback between the two instruments allows for improvedaccuracy and precision, since the same measurement locations can bedetermined and the LCI data can be used to provide an absolute distancescale for the wavefront data at defined locations on the opticalelement. The physical dimensions that are determined include theabsolute thickness profile of the optical element across its surface,the top and bottom surface profiles, and radii of curvature of each ofthe outer surfaces of the optical element. The index of refraction isalso measured. The optical performance characteristics that can bemeasured include optical power, focal length, and optical aberrationsincluding spherical aberration, chromatic aberration, astigmatism, coma,field curvature, and distortion.

Although the apparatus and examples have been described herein asincluding a Shack-Hartmann wavefront sensor SHWFS, it is to beunderstood that other types of wavefront sensors may be utilized in theapparatus shown in FIG. 1. When using other wavefront sensors, lensletarray 105 may be replaced with another type of element. As an example inthe case of a lateral shearing type interferometer setup, lenslet array105 could be replaced with a birefringent crystal.

It is, therefore, apparent that there has been provided, in accordancewith the present invention, a method and apparatus for measuring thedimensions of an optical element, such as a lens. Having thus describedthe basic concept of the invention, it will be rather apparent to thoseskilled in the art that the foregoing detailed disclosure is intended tobe presented by way of example only, and is not limiting. Variousalterations, improvements, and modifications will occur to those skilledin the art, though not expressly stated herein. These alterations,improvements, and modifications are intended to be suggested hereby, andare within the spirit and scope of the invention. Additionally, therecited order of processing elements or sequences, or the use ofnumbers, letters, or other designations therefore, is not intended tolimit the claimed processes to any order except as may be specified inthe claims.

PARTS LIST

-   20 Dual Interferometer-   20 A Autocorrelation Mode Dual Interferometer-   21 Low Coherence Light Source-   22 Laser-   23 light combiner-   24 Circulator-   25 Fiber Stretchers-   26 Optical Fiber-   27 Optical Fiber-   28 Optical Fiber-   29 Optical Fiber-   30 Balanced Detector-   31 Optical Fiber-   32 Optical Fiber-   33 Laser Detector-   34 Laser Light to Detector-   35 Low Coherence Light to Detector-   36 2 By 2 Coupler-   37 Optical Fibers-   38 Optical Fibers-   39 Faraday Rotators-   40 Combined Reference Light Beam-   41 Mirror-   42 Combined Light Beam-   43 Dichroic Beam Splitter-   44 Sample-   45 Laser Light Beam-   46 Low Coherence Light Beam-   47 Faraday Rotator Mirrors-   48 Wavelength Division Multiplexer-   49 Optical Fiber-   50 Detector-   51 Optical Fiber-   52 Optical Fiber-   53 Optical Fiber-   54 Optical Fiber-   55 Wavelength Division Multiplexer-   56 Visible laser-   57 Wavelength Division Multiplexer-   58 Optical Fiber-   59 Optical Fiber-   61 Laser Blocking Filter-   62 Laser Blocking Filter-   63 Low Coherence Light Blocking Filter-   65 Low Coherence Light to Detector-   66 Dichroic Filter-   100 Lens Measurement Apparatus-   101 Lens Being Measured-   102 Cuvette-   102B Cuvette Bottom Section-   102T Cuvette Top Section-   103 Light Source-   104 Second Beam of Light-   105 Lenslet Array-   106 Sensor Array-   107 First Beam of Light-   108 Low Coherence Interferometer-   109 Dichroic Mirror-   110 Lens Central Thickness-   111 Distance between lens bottom surface and cuvette-   112 Computer-   113 Inner Surface of Cuvette Bottom-   114 Lens-   115 Microlens-   116 Lens Concave Surface-   117 Focal Spots-   118 Lens Convex Surface-   119 Display-   120 Shack-Hartman Wavefront Sensor-   121 Solution-   123 Distance Between Lens Top Surface And Cuvette-   124 Inner Surface of Cuvette Top-   125 Cuvette Path Length-   126 Lens Inner Diameter-   127 Lens Outer Diameter-   128 Beam Splitter-   129 Lens Bottom Convex Surface-   130 Optical Probe-   131 Transport Mechanism-   132 Wavefront-   133 Camera Lens-   134 External Image Sensor-   135 Reflected Light Beam-   136 Optical Fiber-   137 Double Convex Lens-   138 Lens Holder Insert-   139 Lens Holder Inner Diameter-   140 Lens Top Convex Surface-   201 Convex Surface Sphere-   202 Concave Surface Sphere-   203 Convex Surface Radius of Curvature-   204 Concave Surface Radius of Curvature-   300 Flowchart-   301 Decision Step-   302 Step-   303 Step-   304 Step-   305 Step-   306 Step-   307 Step-   310 Reference Step-   312 Step-   313 Step-   314 Step-   315 Step-   316 Step-   317 Step-   318 Concurrent Step Indicator-   318A Optional Concurrent Step Indicator-   319 Calculation Dependency Indicator-   320 Step-   321 Step-   322 Step-   323 Step-   324 Step-   325 Step-   326 Step-   327 Step-   400 Flowchart-   410 Step-   420 Step-   430 Step-   440 Step-   450 Step-   455 Repeat Step-   460 Step-   470 Step

1. A method for measuring a lens having a focal length and comprising afirst surface and a second surface defining a lens thicknesstherebetween, the method comprising the steps of: a) measuring thethickness of the lens at a center of the lens with a low coherenceinterferometer; b) measuring the focal length of the lens with awavefront sensor; c) communicating the thickness of the lens and thefocal length of the lens to an analyzer computer; d) calculating aradius of curvature of the first surface of the lens and a radius ofcurvature of the second surface of the lens using an algorithm executedby the computer to obtain dimensions of the lens; and e) performing atleast one of storing in a non-transitory computer storage medium,communicating externally, or displaying the dimensions of the lens. 2.The method of claim 1, wherein the low coherence interferometer isconfigured to direct a first beam of light along a defined axis of thelens and wherein the wavefront sensor is a Shack-Hartmann wavefrontsensor further comprising a light source configured to emit a secondbeam of light and a plurality of lenslets placed in front of a sensorarray.
 3. The method of claim 2, wherein the diameter and location ofthe center of the lens is measured with an image sensor which receives aportion of the second beam of light.
 4. The method of claim 1, furthercomprising the step of calculating at least one optical performanceparameter of the lens.
 5. The method of claim 4, wherein the at leastone optical performance parameter of the lens is selected from opticalpower, spherical aberration, chromatic aberration, astigmatism, coma,field curvature, prism, and distortion.
 6. The method of claim 1,wherein measuring the thickness of the lens at the center of the lensfurther comprises measuring the optical thickness of the lens andcalculating the thickness and index of refraction of the lens. 7-17.(canceled)
 18. The method of claim 6 wherein the step of measuring thethickness of the lens at the center of the lens with a low coherenceinterferometer further comprises installing the lens in the inner volumeof a cuvette and measuring the optical thickness of the lens.
 19. Themethod of claim 18, wherein measuring the optical thickness of thecenter of the lens with the low coherence interferometer furthercomprises measuring an optical path from a top inner surface of thecuvette to a top of the center of the lens and an optical path from abottom of the center of the lens to a bottom inner surface of thecuvette, and calculating the thickness and index of refraction of thelens.
 20. The method of claim 19, further comprising measuring theoptical path from the top inner surface of the cuvette to the bottominner surface of the cuvette at the location of the center of the lensmeasurement location with the lens absent from the cuvette.
 21. Themethod of claim 18 wherein the inner volume of the cuvette contains aliquid medium.